1.	Imagine that you are standing in the middle of Heinz (Acrisure) Field at 12 pm in August. You look up and see the sun shining down on you through a thin layer of cloud. You start to wonder about the atmospheric conditions around you, and you think about how they might be calculated.  Specifically, please calculate the following (a-d). To aid in these calculations, you have the following measurements available to you:
Atmospheric temperature: 32 C
Relative humidity:  56%
Atmospheric Pressure: 1015 hPa

a.	Saturation vapor pressure (es(T)) 


b.	Atmospheric vapor pressure (e) 


c.	Dew point temperature (Td)


To calculate the required values related to atmospheric conditions, we'll use some common equations from thermodynamics and meteorology. Here’s how we can compute the saturation vapor pressure, atmospheric vapor pressure, and dew point temperature based on the given dataTo calculate the required values related to atmospheric conditions, we'll use some common equations from thermodynamics and meteorology. Here’s how we can compute the saturation vapor pressure, atmospheric vapor pressure, and dew point temperature based on the given 

### Given Data:
- Atmospheric temperature (\(T\)): 32°C
- Relative humidity (\(RH\)): 56%
- Atmospheric pressure (\(P\)): 1015 hPa

### a) Saturation Vapor Pressure (\(e_s(T)\)):
The saturation vapor pressure is the pressure exerted by water vapor in air that is saturated (i.e., at the point of condensation) at a given temperature. We can calculate it using **Tetens' formula**:

\[
e_s(T) = 6.112 \times \exp\left(\frac{17.67 \times T}{T + 243.5}\right)
\]

Where \(T\) is in °C and \(e_s(T)\) is in hPa. Let’s calculate it.

### b) Atmospheric Vapor Pressure (\(e\)):
The actual atmospheric vapor pressure can be calculated using the relative humidity (\(RH\)) and the saturation vapor pressure:

\[
e = \left(\frac{RH}{100}\right) \times e_s(T)
\]

Where:
- \(RH\) is the relative humidity in percentage.
- \(e_s(T)\) is the saturation vapor pressure we calculate in part (a).

### c) Dew Point Temperature (\(T_d\)):
The dew point is the temperature at which air becomes saturated (i.e., 100% relative humidity) and water vapor begins to condense into liquid. We use the following approximation for the dew point temperature:

\[
T_d = \frac{243.5 \times \ln\left(\frac{e}{6.112}\right)}{17.67 - \ln\left(\frac{e}{6.112}\right)}
\]

Where \(e\) is the atmospheric vapor pressure calculated in part (b).

Let me now compute each of these values for you.Here are the results based on the given atmospheric conditions:

### a) Saturation Vapor Pressure (\(e_s(T)\)):
\[
e_s(T) = 47.59 \, \text{hPa}
\]

### b) Atmospheric Vapor Pressure (\(e\)):
\[
e = 26.65 \, \text{hPa}
\]

### c) Dew Point Temperature (\(T_d\)):
\[
T_d = 22.14^\circ \text{C}
\]

These values describe the moisture content and saturation conditions in the air at the given temperature and relative humidity.

Do you need further clarification or additional details? Here are 5 related questions to deepen your understanding:

1. How does relative humidity affect the atmospheric vapor pressure?
2. What is the significance of the dew point in weather forecasting?
3. How would a change in atmospheric temperature affect the saturation vapor pressure?
4. Why is the dew point lower than the atmospheric temperature?
5. What would happen to the dew point if the relative humidity were 100%?

**Tip:** The closer the dew point is to the actual air temperature, the higher the relative humidity, which often indicates more humid and uncomfortable conditions.

Imagine that you are standing in the middle of Heinz (Acrisure) Field at 12 pm in August. You look up and see the sun shining down on you through a thin layer of cloud. You start to wonder about the atmospheric conditions around you, and you think about how they might be calculated. Specifically, please calculate the following (a-d). To aid in these calculations, you have the following measurements available to you: Atmospheric temperature: 32 C, Relative humidity: 56%, Atmospheric Pressure: 1015 hPa. a. Saturation vapor pressure (es(T)), b. Atmospheric vapor pressure (e), c. Dew point temperature (Td).

Learn how to calculate the saturation vapor pressure, atmospheric vapor pressure, and dew point temperature based on atmospheric temperature, relative humidity, and pressure measurements. Using thermodynamics and meteorological formulas like Tetens' equation, we solve this real-world problem. Suitable for undergraduate students in atmospheric science.

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